Developing new methods for determining weights of components in network data envelopment analysis

Abstract

Data envelopment analysis (DEA) is a powerful tool for measuring relative efficiency of decision-making units (DMUs). In many cases such DMUs have network structures with internal structures. Traditional DEA models, however, consider DMUs as black boxes without considering their internal structures. Furthermore, overall efficiency in multi component networks is based on efficiencies of their components. Cook et al. (2010) used the additive weighted average of components' efficiencies to calculate overall efficiency. They used the ratio of total weighted input of component to total weighted input of whole components as a weight of component. As an alternative approach, Faramarzi et al. (2014) proposed that the weights are the ratio of total weighted output at the ith component to total weighted output of whole components. In this paper, we propose three novel methods to obtain the weights of components. Then, to compare these three new methods and the methods proposed by Cook et al. (2010) and Faramarzi et al. (2014), we present a case study. Finally, using Spearman's rank correlation coefficient, we analyse the correlation among different approaches.